After getting inside you will see a long cutscene #1, explaining the previous performances including the miraculously cured Joker and showing the death of Talia al Ghul. Curiously, your final enemy won't be Joker, but Clayface #2.
Traditionally it would be good to start with an analysis of Clayface's main offensive skills. He will mostly try to attack you from a distance and depending on the kind of attack he uses you should either evade #1 or perform a counter (Y) #2.
Also try to avoid dodge his jumps #1, escaping from where he'll presumably land #2.
Clayface can be attacked in two main ways. The first implies using the Freeze Blast #1 and it's worth noticing that you won't have to manually aim at the boss as you can also press the right trigger twice. Each hit will take a small part of Clayface's health bar #2.
A much better way of weakening Clayface is standing in the corners of the room, where the explosive materials are. Wait for Clayface to morph into a large ball and starts rolling towards you #1. Dodge in the right moment and Clayface will roll into the explosives, causing it to explode #2.
You have to lead to a situation in which Clayface's is almost fully depleted #1. Continue attacking using the Freeze Blast until you manage to freeze him for a bit #2.
Quickly approach him and press A to grab the sword #1. Afterwards keep repeatedly pressing X #2 for Batman to attack with the blade. Keep doing in until you advance to the second stage of the battle and the boss' energy will refill.
During this part of the battle you will have to dodge not only Clayface's old attacks, but also a couple new types. Most of all, the boss will throw clay projectiles at you. Depending on the type, you have to either jump above them #1 or crouch and wait for them to fly above Batman. Apart from that, look out for his attempts to crush you #2, jump aside fast enough to avoid them.
You have to damage Clayface using the method as before. If there are any explosives left in one of the corners, you can use them as well #1. In case you've used them all up, focus on attacking with the Freeze Blast #2. It's also worth to consider using the Freeze Cluster, of course if you have such in your equipment.
Just like before, you need to keep attacking until you drain of all the boss' health and therefore freeze him #1. Approach Clayface and press A to grab the sword. Afterwards start attacking, making him gradually break up into smaller pieces #2. Another cutscene will start and you will advance to the third and last phase of the battle.
The tactic will completely change during this phase. Start fighting the clay monsters #1, remembering about countering often #2. Note that eliminating them makes the orange health bar to melt down.
The boss will appear himself once you drain the whole orange part of the health bar #1. Use this chance to attack him, using the Freeze Blast for best effect #2.
Clayface will eventually melt down and you will have to fight the clay monster again #1. You need to do exactly the same things as above, so eliminate all the clay enemies and start using ice attacks once Clayface appears #2.
Using this tactic you will gradually drain the blue part of Clayface's health bar. Eventually, after you completely deprive him of energy, he will freeze #1. Quickly run to him and press A to get the cure #2.
Now some cutscenes will play, including numerous surprising moments #1 #2. Congratulations! You have just finished the game!
Notice! Don't forget about being able to continue the game to complete all the challenges and side missions. You can also decide to start a new story in the New Game Plus mode, in which you keep all of you skills and gadgets and have to face the game on the highest difficulty setting.